Let
V={(cost sint )}

and define

(cost 1 sint 1 )⊕(cost 2 sint 2 )=(cos(t 1 +t 2 ) sin(t 1 +t 2 ) )

c ⨀(cost sint )=(cosct sinct )

Show that if ⊕ and ⨀ are the standard componentwise operations, then V is not a vector space.

I'm not quite sure it is not a vector space.

Question

Let 
V={(cost sint  )} 

and define

(cost 1  sint 1   )⊕(cost 2  sint 2   )=(cos(t 1 +t 2 ) sin(t 1 +t 2 )  ) 


c ⨀(cost sint  )=(cosct sinct  ) 

 

Show that if ⊕ and ⨀ are the standard componentwise operations, then V is not a vector space.

I'm not quite sure it is not a vector space.

anonymous · Answer

Well, are you familiar with how you prove that it is not a vector space? Just show that it has more than 1 zero vectors, it is not closed, does not contain a negative for each element, does not have a commutative group operation, or any single of the requirements of a vector space.